5. An electron is trapped in a one-dimensional region of length 1.0 x 10-10 m.(a) How much energy must be supplied to excite the electron from the ground state to the secondexcited state?(b) In the ground state, what is the probability of finding the electron in the region from x=0.09 x10-10 m to 0.11 x 10-10 m? |(c) In the first excited state, what is the probability of finding the electron in the region fromx-0.25 x 10-10 m to 0.50 x 10-10 m?

Answered: Image /qna-images/answer/1b5ec078-c629-409c-aef3-709e7290e121.jpg

Answered: 5. An electron is trapped in a…

Similar questions

1. Louis de Broglie postulated all matter has both a particle and wave nature. The wavelength of any matter wave is given by λ = h/p, where p is the linear momentum p = mv and both p and v are vectors. a) World class marathon runners can run at an average pace of about 3.00 min/km. What is the wavelength, momentum and kinetic energy of a 55 kg runner racing at this average speed? b) What is the uncertainty in the runner's velocity if the position is to be determined within one wavelength?
6. Use Boltzmann distribution to solve this problem. A system consists of 3,000 particles that can only occupy two energy levels: a nondegen- erate ground state of 0.052 eV and a threefold degenerate excited state at 0.156 eV. If T = 900 K, (а) find the number of particles at each energy level. –0156 ev (b) what is the total energy of the system? 0,052 ev
Q²- A system of two energy levels E, and E₁ is populated by N particles at temperature T. The particles populate the energy levels according to the classical distribution law. (a) Derive an expression for the average energy per particle. (b) Compute the average energy per particle vs the temperature as T → 0 and T → co (c) Derive an expression for the specific heat of the system of N particles (d) Compute the specific heat in the limits T→ 0 and T → ∞o.
3. The classical partition function of a gas of noninteracting indistinguishable particles is written as exp{- N! 2m Z= where N is the number of particles of mass m, r, and p, are the position and the momentum of the ith particle, B = 1/(kpT), and Tis the temperature of the gas. The volume of the gas is V. (a) Find the analytic expression of the partition function of the gas. (b) Obtain the total mean energy E of the gas from the partition function. (c) Obtain the entropy S of the gas from the partition function and the total mean energy. Lexp(-x³xdx = Va Hint:
Consider a model of an electron as a hollow sphere with radius R and the electron charge -e spread uniformly over that surface. d. Use Einstein’s equation relating rest mass to energy to derive a value for R. Unfortunately, your answer will be model-dependent. The traditional “Classical radius of the electron” is derived by setting the electrostatic work to be e2/(4pi e0 R)
c) The Bohr model of the atom postulated electrons orbiting around the nucleus in stable orbits. De Broglie explained what orbits could exist by postulating that electrons (and any- thing else) with momentum p have an associated wavelength λ, given by λ=h/p where h is Planck's constant. i) For an electron orbiting around a proton (the Bohr model), equating the centripetal force with the Coulomb force gives the expression v² = e²/(4πεmer). Calculate the speed of an electron orbiting at the Bohr radius, ˜Â = 0.053 nm. ii) Calculate the momenta and the de Broglie wavelengths of the electron of part (i) and of a bird (a racing pigeon) that weighs 0.350 kg and flies at 100 km per hour. iii) Compare the wavelength for the electron that you obtain in (ii) with the circumference of the orbit. Comment on this comparison. Explain briefly what it implies about the other possible orbits of the Bohr model and how the higher orbits might be predicted.
What constraints does the uncertainty principle place on our knowledge of the world? To get a sense of scale, we’ll look at the uncertainty in speed for a confined electron and for a confined dust particle.a. What range of velocities might an electron have if confined toa 0.30-nm-wide region, about the size of an atom?b. A 1.0@mm@diameter dust particle (m ≈ 10-15 kg) is confined within a 5-μm-long box. Can we know with certainty if the particle is at rest? If not, within what range is its velocity likely to be found?
An isolated atom of certain element emits light of wavelength 529 nm when the atom falls from its sixth excited state into its third excited state. The atom emits a photon of wavelength 422 nm when it drops from its seventh excited state into its third excited state. frind wavelength of the light radiated when the atom makes a transition from its seventh to its sixth excited state, in um. a. 21 b. 2.09 c. 2086.34 d 0.0209 e. 208. 63
The wavelength of the emitted photon from the hydrogen molecule H2 is 2.30 μm (micrometers) when the vibrational quantum number decreases by one. What is the effective "spring constant" for the H2 molecule in N/m ?What is the "zero point" energy (in eV) of the molecular vibration?
If a metal has a work function 4.3 eV what is the minimum frequency for photo-emission?A. 3.5 x 108 HzB. 3.0 x 1010 HzC. 10.0 x 108 HzD. 1.04 x 1015 HzE. 1.0 Hz
a) Find the de Broglie wavelength of electrons moving with an average speed of 1.55 x 105 m/s. b) Suppose these electrons are described by a wave packet of width 2.55 nm. What is the uncertainty of the momentum of the electrons?